See UPDATE below, for graphics with descenders.
Here, \scalerel* scales the image to take the same vertical footprint as a capital letter "X". That also means the logo will automatically scale with font size. EDITED to make the process a macro (thanks to Maarten).
\documentclass{article}
\usepackage{scalerel}
\def\mylogo{\scalerel*{\includegraphics{ARL_Logo_March2012_BlackGold}}{X}}
\begin{document}
Can I insert my \mylogo{} inline?
\tiny Can I insert my \mylogo{} inline?
\end{document}

Because the original was a vector image stored in PDF, it zooms without loss of resolution:

UPDATE:
If the original graphic has descenders, one has two options.
One can vertically shift (with a \raisebox) the \includegraphics to match the natural baseline of the graphic with the LaTeX baseline and then "fool" \scalerel* but turning off the depth of shifted graphic:
\documentclass{article}
\fboxsep=-\fboxrule
\usepackage{scalerel}
\def\theirlogo{\scalerel*{%
\setbox0=\hbox{\raisebox{-52pt}{\includegraphics{GoogleLogo}}}\dp0=0pt\box0}{X}}
\begin{document}
Can I insert my \theirlogo{} inline?
\tiny Can I insert my \theirlogo{} inline?
\end{document}

Alternately (and perhaps more efficiently), one could leave the \includegraphics unaltered and add a appropriately sized negative rule (in scalable units) to the second argument of the \scalerel*.
\documentclass{article}
\fboxsep=-\fboxrule
\usepackage{scalerel}
\def\theirlogo{\scalerel*{\includegraphics{GoogleLogo}}{X\rule[-.6ex]{0pt}{1pt}}}
\begin{document}
Can I insert my \theirlogo{} inline?
\tiny Can I insert my \theirlogo{} inline?
\end{document}